BLM 1612 Circuit Theory Prof Dr Nizamettin AYDIN

BLM 1612 - Circuit Theory Prof. Dr. Nizamettin AYDIN naydin@yildiz. edu. tr www. yildiz. edu. tr/~naydin Filters and Bode Plots 1

Filters • Objective of Lecture – Describe the filter types and functions. 2

Filters • Any combination of passive (R, L, and C) and/or active (transistors or operational amplifiers) elements designed to select or reject a band of frequencies is called a filter. • In general, there are two classifications of filters: – Passive filters • series or parallel combinations of R, L, and C elements. – Active filters • transistors and operational amplifiers in combination with R, L, and C elements. 3

Filters • In general, all filters belong to the four broad categories: (a) low-pass, (b) high-pass, (c) pass-band, (d) stop-band 4

R-C LOW-PASS FILTER 5

R-C LOW-PASS FILTER • For filters, a normalized plot is used 6

R-C LOW-PASS FILTER 7

R-C LOW-PASS FILTER 8

R-C LOW-PASS FILTER 9

R-C LOW-PASS FILTER 10

R-C LOW-PASS FILTER • In summary, for the low-pass R-C filter: 11

R-L LOW-PASS FILTER • The low-pass filter response can also be obtained using the R-L combination 12

R-C HIGH-PASS FILTER 13

R-C HIGH-PASS FILTER 14

R-C HIGH-PASS FILTER 15

R-C HIGH-PASS FILTER • In summary, for the high-pass R-C filter: 16

R-L HIGH-PASS FILTER • The highpass filter response can also be obtained using the R-L combination 17

PASS-BAND FILTERS • A number of methods are used to establish the pass-band characteristic. – One method uses both a low-pass and a high-pass filter in cascade. 18

STOP-BAND FILTERS • A number of methods are used to establish the stop-band characteristic. – Stop-band filters can also be constructed using a low-pass and a high-pass filter. 19

Bode Plots • The frequency range required in frequency response is often so wide that it is inconvenient to use a linear scale for the frequency axis. • Standard practice to plot the transfer function on a pair of semilogarithmic plots: – The magnitude in decibels is plotted against the logarithm of the frequency; – The phase in degrees is plotted against the logarithm of the frequency. • Bode plots are semilog plots of the magnitude (in decibels) and phase (in degrees) of a transfer function versus frequency. 20

Example 01… • |H(jω)| vs. Frequency 21

Example 01… • Bode Amplitude Plot 22

(Voltage) Transfer Function 23

Standard Form 24

Decade 25

Bode Plot Procedure 26

Term Types 27

Term Types 28

Term Types 29

Term Types 30

Term Types 31

Term Types 32

Example 02… • Construct a Bode plot for the amplitude and phase of the transfer function that is given 33

…Example 02… • Amplitude plot: 34

…Example 02… • Phase plot: 35

…Example 02… • Amplitude plot - Matlab 36

…Example 02 • Phase plot - Matlab 37

Example 03… 38

…Example 03 39

Idealized Bode plots for various functions 40

Idealized Bode plots for various functions 41

42